LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

BA 11

FIFTH SEMESTER – November 2008

ST 5501 – TESTING OF HYPOTHESIS

 

 

 

Date : 05-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

 

Answer ALL the Questions.                                                                               (10 x 2 =20 marks)

 

1. Define : Best Critical Region
2. What are randomized tests? Give an example of randomized test.
3. Give an example of a family of density functions not having MLR Property.
4. When do you say a density function is a member of one parameter exponential family?
5. What is the fundamental difference between SPRT and other conventional tests?
6. Describe: Likelihood ratio criterion.
7. Mention the statistic used for testing the hypothesis that the population correlation coefficient is zero.
8. Define Confidence level.
9. Define the term run in connection with Non-parametric methods
10. What is Empirical Distribution Function?

 

 

PART – B

 

Answer any FIVE questions.                                                                             (5 x 8 =40 marks)

 

1. State and prove Neyman Pearson lemma
2. Show that Binomial densities are members of one parameter exponential family.
3. Derive the UMPT test of level 0.05 for testing the hypothesis against the alternative based on a single observation drawn from exponential distribution with mean and also obtain its power function
4. Derive the likelihood ratio test for testing  againstbased on a sample of size 17 drawn from when is unknown.
5. Write a descriptive note on SPRT
6. Derive the large sample confidence interval for in the case of exponential distribution with mean
7. Explain run test for randomness.
8. Describe Kolmogrov-Smirnov one sample test

 

 

 

PART – C

 

Answer any TWO questions.                                                                             (2 x 20 =40 marks)

 

1. Derive the MPT of level 0.10 for testing against the alternative in Poisson distribution with mean  based on a sample of size 10 and compute the power of the test.

 

1. Derive the UMPT for testingagainst based on a sample of size n drawn from and also derive its power function.

 

1. Derive the likelihood ratio test for testing the equality of two normal population means assuming that the variances are unknown but equal and the sample sizes are different.

 

 

1. Write short notes on the following:

• Randomised tests vs Nonrandomised tests
• Monotone Likelihood Ratio Property
• Large sample confidence intervals
• Mann-Whitney U Test

 

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